Hi Bruno and Jesse:
At 10:23 AM 12/18/2004, you wrote:
At 21:48 17/12/04 -0500, Hal Ruhl wrote:Can a kernel of information be self inconsistent? From Bruno's last post I think it is possible to impose this idea on the All.
I'm afraid I said the contrary (unless I misunderstand what you are pointing at through the expression "kernel of information"). If you agree that a kernel of information is like a theory or any finitely describable machine, then only such a thing can be said inconsistent.
At this point I have talked myself into the position that since the All is absent information then we have no way to describe it as consistent or inconsistent in the usual logic meaning that I understand. It may contain self inconsistent kernels or pair wise inconsistent kernels but this seems to sum to a neutral position.
Pair wise [or better group wise] inconsistent kernels would differ in the truth value assigned to the same internal component but sum to a neutral position to maintain the overall nature of the All. I am not saying they exist but allow for it.
The "All", I put it on the semantical side, I don't see how that can be made inconsistent in any interesting way. It is *our* attempts to manage the "All" which can lead to our inconsistencies. In case we discover some of those inconsistencies we better should backtrack. I think. No?
I now agree with this as above.
At 11:28 AM 12/18/2004, you wrote:
At 20:39 17/12/04 -0800, Pete Carlton wrote:As usual when I ask a question like this, if the answer is available in a text on logic or elsewhere, please just tell me where to look.
..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here.
For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers.
Remember that comp, as I present it, make "worlds" non computable. It is a consequence of
of the self-duplicability, when distinguishing 1 and 3 person points of view.
Do you mind then a little more non computability re the third person point of view as per my dynamic?
Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera.
However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention.
Indeed, it needs a universal machine, and even an infinity of them. But all that exists and describes by the set of (sigma1) true arithmetical propositions. See Podniek's page
I may not have time left for yet another schooling but I intend to take a much closer look at your material after I resolve my issues with residual information and the origin of the dynamic which this thread might accomplish.
So my question is, what do you mean when you say "a universe that has a sequence of successive states that follow a set of fixed rules?" What could make one state "give rise" to the "next" state? Citing "causality" just gives a name the problem; it doesn't explain it.
I completely agree with you. The primitive "causality" of the comp platonist is just the
"implication" of classical propositionnal logic. Most of the time (sorry for the pun) time of a computation can be described using no more than the axioms of Peano Arithmetic, including especially the induction axioms: that if P(0) is true and if for all x (P(x) ->P(x+1) ) then for all x we have P(x).
(Witten B(0) & Ax(B(x)->B(Sx)) -> AxB(x) in
(S x) is x + 1
As I said in another post I think the idea of one state giving rise to the next creates issues with accumulating algorithmic complexity. However, a sequence in which each state is independent of any other state could look causal for long strings of states.
And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself.
But that "time" can be substituted by natural numbers, enumerating for exemple the states of some universal machine (itself described in arithmetic).
This sounds like kernels to me.
This question doesn't engage with your schema head-on; it's more of a side detour I've thought of asking about many times on the list; I thought it might get explained at some point. Well, now I'm asking.
Now, if you ask where natural numbers comes from, that's a real mystery.
But then I can explain you why no Lobian Machine can solve that mystery, and why, if we want to talk about all the natural numbers, we are obliged to postulate them at the start.
My kernels would be describable by natural numbers so are they actually natural numbers?
At 11:45 AM 12/18/2004, you wrote:
At 03:31 18/12/04 -0500, Jesse Mazer wrote:I don't think Bruno's last post was really implying that "everything" would be inconsistent, I thought his point was more that you can't consider things like the collection of all possible sets to itself be a "set".
Exactly. It is the machine which gives a name to something too big which will take the risk of being inconsistent. The big "all" is not made inconsistent by allowing the possibility of inconsistent machines.
As I said I now agree with this since the All contains no information - see above. As I said in an earlier post the inconsistency I desire to be in the All is not the same as the inconsistency of a kernel.
Actually it is already consistent for a consistent loebian machine to be inconsistent, and this is not only true *about* any consistent Lobian machine, but it is communicable by any of them (provable by G* but already by G). Cf FU.
It is again the second incompleteness theorem: (t = true or "p_>p")
CONSISTENT t -> NOT(PROVABLE(CONSISTENT t)), or by the duality between CONSISTENT and PROVABLE:
CONSISTENT t -> CONSISTENT (NOT (CONSISTENT t))
I think this means that it is consistent for a kernel representing a Loebian machine [I am not pretending I know what a Loebian machine is] to be internally inconsistent.
This next post was from Jesse:
At 11:41 PM 12/18/2004, you wrote:
Hal Ruhl wrote:
I think it would be simpler if you responded directly to quotes from my previous post, rather than just making general statements about issues raised in that post. For example, here you continue to *assert* that there is something inherently time-based about logical statements, but you don't in any way explain what is wrong with my counterargument from that post:
I was still having reading difficulties with my new lenses so this was easier for me.
OK, no problem.
'The laws of logic need not be thought of as rules of "discovery", they can be thought of purely as expressing
"Expressing" seems to be a time dependent process.
I don't think it needs to be. When we say a certain set of symbols "expresses" something, in the most abstract sense we're just saying there's a mapping between the symbols and some meaning.
That would be static information within a kernel.
static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or "discovered" them.
As are my kernels of information.
For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.'
Sure, That is a kernel. Observation does not make a kernel a kernel.
OK, but this isn't really relevant to my question, namely, why does any of this require time?
A kernel does not need a set of rules to make the informational relationships within it what they are. The very words "rules", "laws" and the like carry the implication of a process where the rules and laws are consulted and followed. This is a hidden assumption of some ordered sequence - time. I do not know how to be clearer than that.
Likewise, you didn't address my point that "I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises",
I do not believe that Cantor would be sympathetic with that. I think you need to believe in infinity in order to justify working to understand it and thus justify it.
I believe Bruno said that some information systems included a set of beliefs. As I recall the "premises" are these beliefs. Justification comes from emotions [based on other beliefs] surrounding the resulting system such as simplicity, elegance of apparent explanation etc. So it seems to me that justification is part of belief.
My point is that if I want to demonstrate the truth of some statement X to you (without appealing to new empirical evidence), I look for some set of premises that we *already* share, and then try to show how these premises imply X. I can't think of any historical example where someone's new idea is accepted by other people without the person appealing to common premises they already share. Can you?
See above re "infinity".
and you didn't address my question about whether you think there could be a world/kernel where a vehicle simultaneously
Again time inserts itself as the notion of "simultaneously".
"Simultaneously" shouldn't be taken too literally, "X and Y are simultaneously true" is just a shorthand way of saying that X and Y are truths that both apply to exactly the same domain, whether "same domain" means "same universe", "same time", or whatever. For example, if I say "Ronald Reagan was President of the U.S. in 1985" and "Bill Clinton was President of the U.S. in 1995", these are two non-contradictory truths that apply to the domain of "U.S. history in our universe", so in that sense they are "simultaneous" truths about this domain even though they refer to different dates. On the other hand, if I said "Ronald Reagan was President of the U.S. in 1985" and "Lex Luthor was President of the U.S. in 1985", and both applied to the domain of "U.S. history in our universe", then this would be a contradiction. But if I made clear that the first statement applied to the domain of "U.S. history in our universe" and the second applied to the domain of "U.S. history in an alternate universe" then there would no longer be any contradiction in these statements.
had different numbers of wheels,
If the world was a CA and half the applicable cells were in a two wheel state and half in a three wheel state what would that be?
I can't really picture a CA where the state of a cell specified a number of wheels, but never mind--this would clearly involve no contradiction, because the statements "the cell is in a 2-wheel state" and "the cell is in a 3-wheel state" would not apply to the same domain, since they refer to two *different* cells. There is only a logical contradiction here if both apply to exactly the same domain--in this case, the same cell in the same "world" at a single time.
My intent in the above was for both kinds of cells to be in the same universe. If cells are on the order of the Plank distance in diameter and half of the applicable states were in a two wheel state and the rest in a three wheel state then what would an observer many orders of magnitude larger observe?
Do you think it could be possible for two contradictory statements about the state of a single cell at a single moment in a single world to *both* be true?
I still think that Bruno has allowed for such a case - see above re "Loebian machine".
From the inside perspective we are forced to be in, all we have to justifyShould we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and "Physical Reality" washes over them in some sequentially inconsistent way.
So do believe the statement "the states of all universes don't preexist in the All, and 'Physical Reality' does not wash over them in any sequentially inconsistent way" would be false? If so, it seems that you yourself have the "hubris" to apply the logical law of noncontradiction to statements about reality as a whole.
I am just try to think of the simplest system that contains no information and yet has a dynamic that could support what might be the universe some may believe they inhabit.
But then is there really a process like "think"?
The All as I defined it [my current proposed belief] contains a kernel for the Nothing as well as a kernel for the All thus the nesting.such a belief system is our own beliefs re efficiency, beauty, etc. etc. so our beliefs justify our beliefs. Is this not self referential? I do not intend to impose that on the system as a whole.
You didn't really answer my question above. What I'm asking is, every time you make a statement about reality as a whole, do you intend to deny that the negation of your statement is true? For example, above you say that "The All contains a kernel for the Nothing as well as a kernel for the All." If I make the statement "The All does *not* contain a kernel for the Nothing *or* a kernel for the All", would you then say my statement is false? Please give me a yes-or-no answer to this question, if at all possible.
One has to at least stick with the definitions that establish the system. A zero net information system that actually contains all information would have to contain all kernels. Within the context of my beliefs [permises] then I would answer yes since your statement violates this premise. This is not a matter of the "Laws of Logic" but rather an informational relation within the system. See below re alternate systems
I do not agree with your "rather" based cancelation of the residual information issue since I see it as an unnecessary complication of my own method.
I'm not sure what you mean by "rather based cancellation." If you're talking about my point that every statement could be simultaneously true and false if you throw out the laws of logic, obviously *I* don't believe this is a good way to solve the "residual information issue", since I think it's nonsensical to allow logical contradictions. But since you seem to be saying the laws of logic aren't absolute, I was just pointing out that you would have no basis for denying that statements about reality can be simultaneously true and false. If you say that it is an "unnecessary complication" to allow statements about reality as a whole to be both true and false, then you are in effect saying it would be an unnecessary complication to claim that the laws of logic don't apply to reality as a whole!
I just believe in my own sense of neatness. You gave two apparently contradictory statements which when put in the same pot seem to sum to what I propose for the whole system absent the "rather". I wish to avoid including our "laws of logic" as a necessary component of a kernel.
But if you "wish to avoid" allowing statements about reality to be both true and false, that means you "wish to avoid" allowing reality as a whole to contain logical contradictions! The two ideas are exactly equivalent.
What has that got to do with what I said above? Would both of your statements not be in the same meta system? I can in fact - as I said - accept both because in my opinion they add up to what I am saying. I think there is miscommunication here re the ideas of true, false, logical, contradiction, reality, etc. etc.
My point is that it is more pleasing to think of the dynamic as being inconsistent [each state has no cause effect link of any sort to any other state] if there are other components of the All that are inconsistent. But these are not really the same thing and I begin to think the latter is a side bar issue.
There is nothing "inconsistent" in a logical statement about having no causal links between states--such an idea does not imply any logical contradictions (ie it doesn't imply that two contradictory statements can both be true in precisely the same domain).
I said exactly this when I said "But these are not really the same thing and I begin to think the latter is a side bar issue." right above.
indicated that as much
I think you are misunderstanding what the "laws of logic" really mean, examples like different cells of a cellular automata having different states
See above: Its in the eye of the beholder.
or different states in a series
Where did "series" come from?
having no causal relationship to one another don't contradict the laws of logic in any way.
I was not talking about the "laws of Logic" I was asking if the universe in question did not in fact have a vehicle with both two wheels and three wheels from the point of view of an observer much larger than a cell.
Does that mean you say the statement "each state of the dynamic is completely dependent on the current state" is false?
I believe we should avoid applying logic to a zero internal information entity such as the All. I believe this causes problems.
You didn't answer my question. Would you say the statement "each state of the dynamic is completely dependent on the current state" is false, or would you say it's true, or would you say it is neither true nor false, or what?
How do you justify the question? My quest is zero information in the whole system. I established a system I believe meets this criteria. Its premises could I suppose be taken as "true" without proof in the usual manner. However, if my system indeed has no information how do the "laws of logic", "truth", "contradiction", etc apply to no information by any justification? Any other premise set establishes an alternate system. Am I to presuppose that there is not a meta system that has more than one zero information system in it or that such a system could not somehow contain a negation of one or all of my premises? See also above.
As to does mathematics contain information, mathematics has the potential to erect boundaries so by my definition it is information.
But doesn't *any* statement you make about reality as a whole, like "each state of that dynamic has to be completely independent of the current state", erect a "boundary" between itself and its negation, in this case "each state of the dynamic is completely dependent on the current state"?
I distinguish between actual boundaries and the potential to erect one.
The All is full of boundaries between kernels but has no potential to erect more. In your "dependent" case one has to manage the dependency rules - a necessary potential to erect boundaries.
How about the statement "The All is full of boundaries between kernels but has no potential to erect more". Isn't there a "boundary" between this statement and its opposite, namely "The All contains no boundaries between kernels but does have potential to erect more"?
Interestingly enough given the way I define information that may be a seed of a meta system such as I mention above.
Would you say the first statement is true and the second is false?